Of course they should.

They own the team, so they should have the most power. Do the players own the owner? No. The owner owns them. Therefore, the players should be thankful that they are playing in the team instead of complaining about having less power. This was an easy discussion. If you disagree, then change your mind.

No, the fans need to have the most power

Fans, they are the ones that should be in charge and have more power then anyone in this. A good example was during the NHL labor dispute, the only people who lost had been the fans, they lost out on their chance, they lost out on their sport and they lost out on something that they love.

No. There should be relatively even split.

The times when owners had more power than the "workers" was the industrial revolution, which was clearly a social disaster in the eyes of many historians. While the same rules might not apply to sports, it is clear that the players ought to have at least a significant say in their own affairs even if the rights of the owners are supposedly indisputable.

No, it should be a fair split

Actually the fans should be the one on top of the totem poll. But the players and the owners should possibly think about it this way, there needs to be a half and half split with the realization that the fans are the ones that need to be heard and people need to realize they are in charge.

No, not if the players are thinking correctly

This seems like a question that is up to the players, actually. You would think that players would know they are the ones doing the job, they are the ones at risk for injury, why should they give up their power to owners? If players organized they would be able to negotiate for whatever they need to effectively play.